Need much more information. 78% RH supply air sounds reasonable. %RH right off the cooling coil should be close to 100%. A typical approach is to over-cool and then re-heat the air. Again, we need much more information in order to help. What kind of space is it? What temperature and humidity are you trying to maintain? Do you have a good vapor barrier? Is there something in the room that is producing a lot of moisture?
Two options: raise temperature in the room to lower R.H. or dehumidify the room with a humidifier. But first as stated above what is the cause of the humidity?
To effectively remove the moisture once its already in the room you have to bring in a lot of constant dry air to absorb the moisture (or be recirculating air through a dehumidifier with a drain). Once the moisture is baked into something though, you have to apply heat energy direct to the moisture source to get it all to effectively release into your dry air stream.
However, if you have fungus on the ceiling and wall - you should be removing and replacing those ceilings and walls. Then before you put in the new ones you need to find your moisture source (and reduce or eliminate it) and then install a system that properly dehumidifies.
